[en] The Advanced Photon Source (APS) will be a third-generation synchrotron radiation (SR) user facility in the hard x-ray regime (10--100 keV). The design objectives for the 7-GeV storage ring include a positron beam natural emittance of 8 x 10^-9 m-rad at an average current of 100 mA. Proposed methods for measuring the transverse and longitudinal profiles will be described. Additionally, a research and development effort using an rf gun as a low-emittance source of electrons for injection into the 200- to 650-MeV linac subsystem is underway. This latter system is projected to produce electron beams with a normalized, rms emittance of ∼2 π mm-mrad at peak currents of near one hundred amps. This interesting characterization problem will also be briefly discussed. The combination of both source types within one laboratory facility will stimulate the development of diagnostic techniques in these parameter spaces